All categories

2 years ago

Simplify (10j+5k)+6j. What 2 properties did you use to to simplify the expression?

Mathematics

1 answer:

Artemon [7]2 years ago

8 0

Answer:

16j+5k

Associative property

Communitive Property (I think)

Step-by-step explanation:

(10j+5k)+6j =

(10j+6j)+5k =

16j+5k

You might be interested in

Use the triangle below to find cos V.

Semenov [28]

Answer:

$cos\ V = \frac{2\sqrt{29}}{29}$

Step-by-step explanation:

Given

The attached triangle

Required

Find cos V

In trigonometry:

$cos\theta = \frac{Adjacent}{Hypotenuse}$

In this case:

$cos V= \frac{TV}{UV}$

Where

$TV = 6$

and

$UV^2 = TV^2 + TU^2$ -- Pythagoras

$UV^2 = 6^2 + 15^2$

$UV^2 = 261$

Take square roots

$UV = \sqrt{261$

$UV = \sqrt{9*29$

$UV = \sqrt{9} *\sqrt{29$

$UV = 3\sqrt{29$

So:

$cos V= \frac{TV}{UV}$

$cos\ V = \frac{6}{3\sqrt{29}}$

$cos\ V = \frac{2}{\sqrt{29}}$

Rationalize:

$cos\ V = \frac{2}{\sqrt{29}}*\frac{\sqrt{29}}{\sqrt{29}}$

$cos\ V = \frac{2\sqrt{29}}{29}$

8 0

2 years ago

Dave receives a salary of $200 a week plus a commission of 10% of his weekly sales. An equation y=mx+b represents Dave’s weekly

eduard

Answer:
Dave makes $350

Explanation:
In order to find this answer, we must first establish the equation for his earnings.
We use slope intercept form:
y = mx + b,
where m = slope and b = y-intercept.

Since the problem states that his commission percentage is the slope and his base salary is the y-intercept, we can use them in the equation to get the following: 
y = 0.1x + 200.

Now knowing that the x is the amount he sells, we can use the $1500 as x to find his total pay for the week:.
y = 0.1(1500) + 200,
y = 150 + 200,
y = 350.

6 0

2 years ago

Read 2 more answers

According to the data, Vannessa mean quiz ...

damaskus [11]

Answer: x = 108

Given the below equation

x + 13 1/2 = 121 1/2

Firstly, we need to convert the mixed fraction into an improper fraction

$\begin{gathered} x\text{ + 13}\frac{1}{2}\text{ = 121 }\frac{1}{2} \\ 13\frac{1}{2}\text{ = }\frac{(2\text{ x 13) + 1}}{2} \\ 13\text{ }\frac{1}{2}\text{ = }\frac{26\text{ + 1}}{2} \\ 13\frac{1}{2}\text{ = }\frac{27}{2} \\ 121\frac{1}{2}\text{ = }\frac{(2\text{ x 121) + 1}}{2} \\ 121\frac{1}{2}\text{ = }\frac{243}{2} \\ \text{Therefore, the new equation becomes} \\ x\text{ + }\frac{27}{2}\text{ = }\frac{243}{2} \\ \text{Isolate x} \\ x\text{ = }\frac{243}{2}\text{ - }\frac{27}{2} \\ \text{Common denominator = 2} \\ x=\text{ }\frac{243\text{ - 27}}{2} \\ x\text{ = }\frac{216}{2} \\ x\text{ = 108} \end{gathered}$

8 0

10 months ago

Use the rule provided to generate the first five terms of the sequence. The rule is 4n + 5.

lesya692 [45]

Answer:

9, 13, 17, 21,25

Step-by-step explanation:

n=1, 4×1+5=9

n=2, 4×2 +5=13

n=5, 4×5 + 5= 25

4 0

2 years ago

A. Solve the differential equation <img src="https://tex.z-dn.net/?f=y%27%3D2x%20%5Csqrt%7B1-y%5E2%7D%20" id="TexFormula1" title

kirill [66]

$y' = \frac{dy}{dx}$

seperable differential equations will have the form
$\frac{dy}{dx} = F(x) G(y)$

what you do from here is isolate all the y terms on one side and all the X terms on the other
$\frac{dy}{G(y)} = F(x) dx$
just divided G(y) to both sides and multiply dx to both sides

then integrate both sides
$\int \frac{1}{G(y)} dy = \int F(x) dx

$

once you integrate, you will have a constant. use the initial value condition to solve for the constant, then try to isolate x or y if the question asks for it

In your problem,
$G(y) = \sqrt{1-y^2}

F(x) = 2x$

so all you need to integrate is
$\int \frac{1}{\sqrt{1-y^2}} dy = \int 2x dx$

5 0

3 years ago